I suppose that’s true, but this kind of confirms my intuition that there’s something funky going on here that isn’t accounted for by rationalist-empiricist-reductionism. Like why are time translations so much more important for our general work than space translations? I guess because the sun bombards the earth with a steady stream of free energy, and earth has life which continuously uses this sunlight to stay out of equillbrium. In a lifeless solar system, time-translations just let everything spin, which isn’t that different from space-translations.
Ah, so I think you’re saying “You’ve explained to me the precise reason why energy and momentum (i.e. time and space) are different at the fundamental level, but why does this lead to the differences we observe between energy and momentum (time and space) at the macro-level?
This is a great question, and as with any question of the form “why does this property emerge from these basic rules”, there’s unlikely to be a short answer. E.g. if you said “given our understanding of the standard model, explain how a cell works”, I’d have to reply “uhh, get out a pen and paper and get ready to churn through equations for several decades”.
In this case, one might be able to point to a few key points that tell the rough story. You’d want to look at properties of solutions PDEs on manifolds with metric of signature (1,3) (which means “one direction on the manifold is different to the other three, in that it carries a minus sign in the metric compared to the others in the metric”). I imagine that, generically, these solutions behave differently with respect to the “1″ direction and the “3” directions. These differences will lead to the rest of the emergent differences between space and time. Sorry I can’t be more specific!
Why assume a reductionistic explanation, rather than a macroscopic explanation? Like for instance the second law of thermodynamics is well-explained by the past hypothesis but not at all explained by churning through mechanistic equations. This seems in some ways to have a similar vibe to the second law.
I suppose that’s true, but this kind of confirms my intuition that there’s something funky going on here that isn’t accounted for by rationalist-empiricist-reductionism. Like why are time translations so much more important for our general work than space translations? I guess because the sun bombards the earth with a steady stream of free energy, and earth has life which continuously uses this sunlight to stay out of equillbrium. In a lifeless solar system, time-translations just let everything spin, which isn’t that different from space-translations.
Ah, so I think you’re saying “You’ve explained to me the precise reason why energy and momentum (i.e. time and space) are different at the fundamental level, but why does this lead to the differences we observe between energy and momentum (time and space) at the macro-level?
This is a great question, and as with any question of the form “why does this property emerge from these basic rules”, there’s unlikely to be a short answer. E.g. if you said “given our understanding of the standard model, explain how a cell works”, I’d have to reply “uhh, get out a pen and paper and get ready to churn through equations for several decades”.
In this case, one might be able to point to a few key points that tell the rough story. You’d want to look at properties of solutions PDEs on manifolds with metric of signature (1,3) (which means “one direction on the manifold is different to the other three, in that it carries a minus sign in the metric compared to the others in the metric”). I imagine that, generically, these solutions behave differently with respect to the “1″ direction and the “3” directions. These differences will lead to the rest of the emergent differences between space and time. Sorry I can’t be more specific!
Why assume a reductionistic explanation, rather than a macroscopic explanation? Like for instance the second law of thermodynamics is well-explained by the past hypothesis but not at all explained by churning through mechanistic equations. This seems in some ways to have a similar vibe to the second law.